Numerical methods for the quantification of the mechanical properties of crystal aggregateswith morphologic and crystallographic texture

  • T. BöhlkeEmail author
  • F. Fritzen
  • K. Jöchen
  • R. Tsotsova
Finite element technology and multi-scale methods for composites, metallic sheets and coating behaviour models: R. Alves de Sousa, R. Valente, L. Duchêne, V. Kouznetsova


The influence of an anisotropic distribution of crystal orientations and an anisotropic average grain shape is analysed using finite element simulations. By the numerical approach, which is based on a statistical volume element with periodic microstructure and periodic boundary conditions, the influence of the crystallographic and the morphologic texture can be separated by combining (an)isotropic orientation distributions with (an)isotropic grain morphologies.


Crystallographic texture homogenization morphologic texture Voronoi tesselation 


  1. 1.
    M. Ostoja-Starzewski. Material spatial randomness: From statistical to representative volume element. Probabilistic Engineering Mechanics, 21:112–132, 2006.CrossRefGoogle Scholar
  2. 2.
    J.W. Hutchinson. Bounds and self-consistent estimates for creep of polycrystalline materials. Proc. R. Soc. Lon., A 348:101–127, 1976.zbMATHCrossRefGoogle Scholar
  3. 3.
    T. B¨ohlke. The Voigt bound of the stress potential of isotropic viscoplastic fcc polycrystals. Archive of Mechanics, 56(6):423–443, 2004.Google Scholar
  4. 4.
    T. Gnäupel-Herold, P. C. Brand, and H. J. Prask. Calculation of single-crystal elastic constants for cubic crystal symmetry from powder diffraction data. J. Appl. Cryst., 31:929–935, 1998.CrossRefGoogle Scholar
  5. 5.
    S. Kumar and S.K. Kurtz. Simulation of material microstructure using a 3d Voronoi tesselation: Calculation of effective thermal expansion coefficient of polycrystalline materials. Acta Metallurgica et Materialia, 42(12):3917–3927, 1994.CrossRefGoogle Scholar
  6. 6.
    F. Barbe, L. Decker, D. Jeulin, and G. Cailletaud. Intergranular and intragranular behavior of polycrystalline aggregates. Part 1: F.E. Model. International Journal of Plasticity, 17:513–536, 2001.zbMATHCrossRefGoogle Scholar
  7. 7.
    F. Fritzen, T. B¨ohlke, and E. Schnack. Periodic three-dimensional mesh generation for crystalline aggregates based on voronoi tessellations. to appear in Computational Mechanics, 2008. doi:  10.1007/s00466-008-0339-2.
  8. 8.
    U.F. Kocks, C.N. Tome, and H.R. Wenk. Texture and in Polycrystals, Anisotropy: Preferred Orientations and Properties, Their Effect on Materials. Cambridge Univ. Pr., 1998.Google Scholar

Copyright information

© Springer/ESAFORM 2009

Authors and Affiliations

  • T. Böhlke
    • 1
    Email author
  • F. Fritzen
    • 1
  • K. Jöchen
    • 1
  • R. Tsotsova
    • 1
  1. 1.Chair of Continuum Mechanics, Institute of Engineering MechanicsUniversity of Karlsruhe (TH)KarlsruheGermany

Personalised recommendations